Having a very hard time in my PRECALC CLASS

• DeepSpace9
The 6 comes from the fact that the original problem has a factor of (4x+5)^2, which is equivalent to (2)(2)(4x+5)^2. So when that is factored out, it leaves a coefficient of 6. In summary, the student is having trouble with a precalculus problem involving factoring and simplifying expressions. They are confused about where certain numbers came from in the given solution and are seeking clarification. The expert explains that the numbers were factored out and rearranged to make the solution more clear and straightforward.
DeepSpace9
Having a very hard time in my PRECALC CLASS.
When they facto problems they start pulling numbers out of numbers that aren't there..
Example..

3(4x+5)^2 (4)(5x+1)^2 + (4x+5)^3 (2) (5x+1)(5)

Professor said this was the answer.

a) 2(4x+5)^2(5x+1)[6(5x+1)+5(4x+5)]
=
b) 2(4x+5)^2(5x+1)[50x+31] (After combining like terms)

My questions is

Where I labeled a) where did she get the 6 from and the 5 from?
I can see she got the 5 from the original problem, but I thought if she factored out a 2 as a GCF the 5 would be reduced to a smaller number, and the 6 comes out of no where.. HELP

Thanks for the help guys.

Hey DeepSpace9.

Recall that 3*4 = 12 = 6*2 and 5*2 = 10 = 5*2 [Look at the factorization again carefully with the hint mentioned]

So the 6 comes from the fact that (3)(4) = 12 and since I factor out a (2) I would need a (6) to = 12 again? I didn't think we could use a 6 since it was not in the original problem.

Yes that's pretty much it.

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